On Estimating the Parameters of the Bivariate Normal Distribution | ||
| The Egyptian Statistical Journal | ||
| Article 2, Volume 45, Issue 2, December 2001, Pages 143-154 PDF (5.09 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2001.313810 | ||
| Authors | ||
| Ahmed M.M. Sultan* 1; Albert H. Moore* 2; Hala Mohamed Khaleel* 3 | ||
| 1Egyptian Air Force. Cairo, Egypt | ||
| 2Aire Force Institute of Technology, Ohio | ||
| 3Zagazig University | ||
| Abstract | ||
| A technique is applied to estimate the parameters of the bivariate normal distribution with unknown mean vector and unknown covariance matrix by minimizing the Cramer von Mises distance from a non-parametric density estimate and the parametric estimate at the order statistics. The maximum likelihood estimators were found and a comparison was made with the proposed estimator. For different parameters of the true density the proposed estimators were tested using a Monte Carlo experiment. The results show an improvement in mean integrated square error which is taken as a measure of the closeness of the estimated density and the true density. | ||
| Keywords | ||
| The Bivariate Normal Distribution; The Cramer Von Mises Distance; Maximum Likelihood; Monte Carlo | ||
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